The transient rise of a bubble subject to shape or volume changes

This paper deals with two problems in which the rectilinear rise of a gas bubble in a liquid undergoes a transient behavior. In the first problem, the bubble is released with a spherical, oblate, prolate, or oval shape and its evolution to steady state is simulated numerically. Contrary to some recently reported experiments, it is found that the terminal velocity and final shape are independent of the initial shape. This result suggests that the experimental observations may be influenced by uncontrolled effects rather than a genuine multivaluedness of the fluid-dynamic solution for a steadily rising bubble. The second problem concerns the ascent of a bubble which expands, or contracts, due to a change in the ambient pressure. The ensuing behavior of the rise velocity is strongly influenced by added mass effects.

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